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Solving Bayesian inverse problems from the perspective of deep generative networks

Hou, Thomas Y. and Lam, Ka Chun and Zhang, Pengchuan and Zhang, Shumao (2019) Solving Bayesian inverse problems from the perspective of deep generative networks. Computational Mechanics, 64 (2). pp. 395-408. ISSN 0178-7675.

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Deep generative networks have achieved great success in high dimensional density approximation, especially for applications in natural images and language. In this paper, we investigate their approximation capability in capturing the posterior distribution in Bayesian inverse problems by learning a transport map. Because only the unnormalized density of the posterior is available, training methods that learn from posterior samples, such as variational autoencoders and generative adversarial networks, are not applicable in our setting. We propose a class of network training methods that can be combined with sample-based Bayesian inference algorithms, such as various MCMC algorithms, ensemble Kalman filter and Stein variational gradient descent. Our experiment results show the pros and cons of deep generative networks in Bayesian inverse problems. They also reveal the potential of our proposed methodology in capturing high dimensional probability distributions.

Item Type:Article
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Zhang, Pengchuan0000-0003-1155-9507
Additional Information:© Springer-Verlag GmbH Germany, part of Springer Nature 2019. Received: 1 February 2019 / Accepted: 20 May 2019. The research of T. Y. Hou, K. C. Lam, and S. Zhang was in part supported by an NSF Grant DMS-1613861. We would also like to thank Microsoft Research for providing the computing facility in carrying some of the computations reported in this paper.
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Subject Keywords:Uncertainty quantification · Bayesian inverse problem · Machine learning
Issue or Number:2
Record Number:CaltechAUTHORS:20190620-093003600
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Official Citation:Hou, T.Y., Lam, K.C., Zhang, P. et al. Comput Mech (2019) 64: 395.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96584
Deposited By: George Porter
Deposited On:20 Jun 2019 18:01
Last Modified:03 Oct 2019 21:23

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